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Engineering economics is fundamental in engineering, especially for manufacturing support. For simplicity, I am using the term here as a process engineer for printed circuit equipment and automation of production. *Principles of Engineering Economy*^{[1]}, written by Stanford University Professor Dr. Grant Ireson, is the text that I used and one of the basics for understanding engineering economics.

**Interest Variables**

Here are the five primary variables that make up all of the interest formulas for the time value of money:

**I = interest rate per period**

**n = number of interest periods**

**PV = present sum of money**

**FV = future sum of money after** **n** **periods at i interest**

**PMT = end of period payment**

All of these calculations lend themselves for use in spreadsheets and are found as part of MS Excel.

**Interest Formulas**

The interest formulas for these calculations are defined and seen below. For some reason, each of these formulas have been given a specific name and abbreviation. Single amounts do not have an apostrophe after the three-letter-acronym (tla). A series of amounts have the apostrophe (‘). The short-cut way of writing this out is to use this form:

(tla-interest rate-period) seen as: (caf’-6%-10)

- Single Payment-Compound Amount Factor (caf’) for future value (FV) based on the present value (PV):

** FV=PV(1+i)^n ** **(caf')**

- Single Payment-Present Worth Factor (pwf’) for present value (PV) based on the FV

**PV=FV[1/(1+i)^n] (pwf')**

- Series Sinking fund factor (sff) for series payment (PMT) based on the FV

** PMT=FV[i/(1+i)^n-1] ** **(sff)**

- Series Compound Recovery Factor (crf) for series payment (PMT) based on the PV

**PMT=PV[i(1+i)^n/(1+i)^n-1]**** ** **(crf)**

or **PMT=PV[i/{(1+i)^n-1}+i]**

- Series Compound Amount Factor (caf) for future value based on the payments

**FV=PMT[(1+i)^n-1/i] (caf)**

- Series Present Worth Factor (pwf) for PV based on the series of payments

**PV=PMT[(1+i)^n-1/i(1+i)^n]**** ** **(pwf)**

Or **PV=PMT[1/{i/(1+i)^n-1}+i]**

**Examples using Three Variables**

You can see how all of these financial formulas are related by looking at the examples in Figure 1. We start with just three variables: present value (PV) = $1000; period of 10 years (N); and annual interest rate of 6%.

1. We start with $1000 (PV) and want to know what it is worth after 10 years with an interest rate of 6% per year. The caf’ equation is used: (caf’-6%-10). The future value (FV) is $1791.

2. What if we want to know what the FV would be if we withdraw it six years early? The pwf’ is used: (pwf’-6%-6) and the PV is $1263.

3. What PV would it take seven years earlier to get this $1263? Again, pwf’ is used: (pwf’-6%-7) and a PV of $840 would be required.

4. If we took the $840 and invested it over 10 years what payments would we receive at 6% interest? The crf is used (crf-6%-10) to get a payment (PMT) of $114/period.

5. If instead we made payments of $114 per period for 10 years, what would that be worth now? The caf equation is used (caf-6%-10) and the future value (FV) is $1504.

6. What annual payment is required to get $1504 over seven years? The sff equation is used (sff-6%-7) and PMT would be $179/ year.

7. What present value would $179 in interest income at 6% give us over seven years? The pwf is used (pwf-6%-7) and the V is $1000, the same as we started with.

**Figure 1: Seven financial calculations all involving $1000 at 6% interest over various years.**

**Important Engineering Metrics**

**ROI**(return on investment) is the equivalent bank interest rate of all the money you spent and all the profits you made over a fixed time span**NPV**(net present value) is the current value of all the cash flows over time assuming cash is worth, x %, say 3 % as an interest rate.**BET**is the breakeven time (or the time to money) before the profits you gain pay for all that you spent to get the profits. Or, how long before you truly make a PROFIT?**TVM**is the time value of money. Because of inflation, future money is worth less than current money, or it is discounted.**DEPRECIATION**is the value of equipment that the government lets you deduct each year as equipment gets older. This encourages you to buy new equipment. Some may be depreciated very fast, perhaps in three years instead of five.

The common practice in equipment justification is to calculate the ROI or the NPV of the cash flows associated with implementing the equipment, including all purchases of equipment, installation, taxes (depreciation), water treatment savings and operating costs against the labor saving, and yield improvement by NOT installing automation.

The rate of return is easiest calculated by Excel. To do it manually requires a trial-and-error calculation of assuming an interest rate (I) over the period of the investment (n) and calculating the compound recovery factors (crf) for each year. When the sum of all the crfs equals the initial investment, then the interest rate is the ROI.

The NPV is easier to calculate. It is the present worth factor (pwf) for all the cash flows each year for the life of the investment using current or future interest rates.

The classical trade-off is between the purchase of an automated system (and its advantages) and the continued increase in direct labor. But quality, process yields and waste water treatment costs also enter into the calculation. Return on investment is the calculation of the equivalent interest rate of all the moneys invested based on all the cash flows over the useful life of the equipment.